Investigating the hidden geometry system at the entrance of the historical houses of Kashan from the Qajar period to the beginning of the Pahlavi period
Abstract
Geometry is one of the most important aspects hidden in the design of historical buildings in a way, it can be said that architecture without the presence of geometry is meaningless and lacks functional validity. The ratio and proportion that can be seen in the entrance and front facade of the historical houses of Kashan is a function of geometry, which is named hidden geometry in this research. The geometric system at the entrance of historical houses is one of the most important topics that help to better understand the historical building. The findings show that the entrance design of the houses is under the hidden geometry system, and five types of geometric systems are used to shape it, including symmetry, Fibonacci in golden triangles, Fibonacci in golden rectangles, dynamic rectangles, and regular polygons.
Keyword : historical houses, entrance gate, hidden geometry, golden proportions
How to Cite
Danaeinia, A., Erfan, B., & Mohamadi Sabet, Z. (2024). Investigating the hidden geometry system at the entrance of the historical houses of Kashan from the Qajar period to the beginning of the Pahlavi period. Journal of Architecture and Urbanism, 48(1), 67–82. https://doi.org/10.3846/jau.2024.21046
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Abbasi, N., Valibeig, N., & Arya, N. (2021). A comparative study of the entrance circulation of Abbasi Jame’ Mosque and Seyyed Jame’ Mosque in Isfahan from the perspective of the Persian Geometric proportion in an architectural plan. CIAUJ, 6(1), 39–51. https://doi.org/10.52547/ciauj.6.1.39
Afradi, K. (2018). Categorizing the design and manufacturing methods of doors and portals in historical structures of rasht from Qajar period until now. Pazhohesh-ha-ye Bastanshenasi Iran, 7(15), 203–218.
Ajami, S., Shahroudi Bahnamiri, A., & Lashgari, R. (2023). Evaluation of the geometric shape of windows in the residential houses with neuroscience approach. Journal of Architectural Thought, 7(13), 155–173.
Akhtaruzzaman, M., & Shafie, A. A. (2011). Geometrical substantiation of Phi, the Golden Ratio and the baroque of nature, architecture, design and engineering. International Journal of Arts, 1(1), 1–22. https://doi.org/10.5923/j.arts.20110101.01
Alsina, C., & Nelsen, R. B. (2010). Charming proofs: A journey into elegant mathematics. Mathematical Association of America. https://doi.org/10.5948/UPO9781614442011
Azar Khordad, F., Hashemi Zarjabad, H., & Zarei, A. (2018). Analysis of applied geometry in the plan of three buildings Abubakr Taybadi, Goharshad Mosque and School of Ghiasieh Khargerd. Parseh Journal of Archaeological Studies, 2(4), 121–136. https://doi.org/10.30699/PJAS.2.4.121
Boettger, T. (2014). Threshold spaces: Transitions in architecture: Analysis and design tools (H. Labies-Volz, Trans.). Walter de Gruyter GmbH. https://doi.org/10.1515/9783038214007
Borges, R. F. (2004). The Phi code in nature, architecture and engineering. WIT Transactions on Ecology and the Environment, 73, 401–409.
Bressler, J. (2020). The ubiquity of Phi in human culture & the natural world. John Carroll University. https://collected.jcu.edu/mastersessays/132
Brown, C. (2008). Fibonacci analysis. Bloomberg Press.
Cui, P., & Huang, M. (2012). Studies on building entrance cold adaption design and structure in cold region – Take Harbin Institute of Architecture as example. Applied Mechanics and Materials, 226–228, 2407–2411. https://doi.org/10.4028/www.scientific.net/AMM.226-228.2407
Danaeinia, A. (2021). The sense of entrance to a place in Kashan historical houses. Journal of Architecture and Urbanism, 45(1), 38–49. https://doi.org/10.3846/jau.2021.13209
Danaeinia, A., & Erfan, B. (2023). The system of theoretical geometry of the two-leged plumb tier of Rasmi-Bandi derived from peripheral circle in Persian architecture. Journal of Conservation and Architecture in Iran, 13(33), 57–76.
Daneshmand, S., & Noghrekar, A. (2012). How to design the entrance of the building according to the principles of the formation of barrier architecture. Journal of Studies on Iranian - Islamic City, (9), 79–89.
Dewitte, L. (2015). Proportionality in the architecture of Dom Bellot. Nexus Network Journal, 17, 457–485. https://doi.org/10.1007/s00004-015-0246-8
Dousti Motlagh, P. (2009). The study of entrance history. Armanshahr Architecture & Urban Development, 2(2), 91–104.
Dunlap, R. A. (1997). The Golden Ratio and Fibonacci numbers. World Scientific Publishing. https://doi.org/10.1142/3595
El-Said, I., & Parman, A. (2008). Geometric concepts in Islamic art (3rd ed., M. Rajabnia, Trans.) Soroush Press.
Farshchi, H., & Majidi, M. (2021). Investigation of the architectural system and geometric proportions of the central courtyard and its walls in the historical houses of Kashan (Case study: Ten historical houses of the Qajar period in Kashan). Culture of Islamic Architecture and Urbanism Journal of Environmental Studies, 6(2), 95–112. https://doi.org/10.52547/ciauj.6.2.95
Feizollahbeig, A., Golabchi, M., & Reza-Zadeh, M. (2021). An investigation in geometry and proportion in relation to structural system in buildings with discontinuous double shell domes in Tafresh region. Soffeh, 31(3), 21–42. https://doi.org/10.52547/sofeh.31.3.21
Fun, T. L., Usman, I. M. S., Utaberta, N., Ariffin, A. R. M., & Sharif, R. (2021). The importance and potential of Golden Ratio in architecture design. Journal of Xi’an University of Architecture & Technology, 13(1), 477–502.
Ganjavie, A. (2003). City entrance of Kerman [Thesis]. Islamic Azad University.
Ghorbani, H. (2021). Golden Ratio: The mathematics of beauty. Mathematics Interdisciplinary Research, 6(2), 159–170.
Gjonbalaj, A., Oliv, D., Lotter, G., & Dalzell, M. (2021). The golden ratio and its effects on the perceived visual appeal of photos. Journal of Student Research, 10(1), 1–13. https://doi.org/10.47611/jsrhs.v10i1.1346
Grütter, J. K. (2009). Ästhetik der architektur (5st ed., Pakzad and A. Homayun, Trans.). Publications Center of Shahid Beheshti University.
Havil, J. (2012). The irrationals: A story of the numbers you can’t count on. Princeton University Press. https://doi.org/10.1515/9780691247670
Javadi Nodeh, M., Shahcheraghi, A., & Andalib, A. (2022). An investigation of the golden proportions and geometric principles derived from nature in the structural components of the traditional houses (Case study: Qajar houses in Ardabil). Bagh-e Nazar, 19(100), 35–48.
Kalantari, N. N., Etesam, I., & Habib, F. (2017). Check in architectural geometry and proportions of the golden Iran (Case study: Tabriz traditional houses). Urban Management, 16(46), 477–491.
Katyal, P., Gupta, P., Gulati, N., & Jain, H. (2019). A compendium of Fibonacci ratio. Journal of Clinical and Diagnostic Research, 13(11), 3–10. https://doi.org/10.7860/JCDR/2019/42772.13317
Karimi Khorasani, K. (2017). Analyze of geometric proportions and structure of girih tiles in portals of schools and shrines of Isfahan (Case study: Nimavar school and Darb-e Imam shrine) [Thesis]. Art University of Isfahan.
Khamechian, A., Azad, M., & Tahbaz, M. (2018). Geometric analysis and proportions of Orosi Windows’s Case study: 7 Orosi of Kashan houses. Journal of Iranian Handicrafts Studies, 2(1), 5–23. https://doi.org/10.22052/1.2.5
Koshy, T. (2018). Fibonacci and Lucas numbers with applications (2nd ed., Vol. 1). John Wiley & Sons, Inc. https://doi.org/10.1002/9781118742297
Krier, R. (2001). Architectural proportions (1st ed., M. Ahmadinejad, Trans.). Nashre Khak.
Larsen, S. H. (2021). DNA structure and the golden ratio revisited. Symmetry, 13(10), Article 1949. https://doi.org/10.3390/sym13101949
Lawlor, R. (1982). Sacred geometry: Philosophy and practice (1st ed.). Thames & Hudson Ltd.
Moblian, E., & Kianmehr, G. (2014). The influence and adaptation of the role of Sasanian motifs on the motifs of the front of the mosque of Jurgir al-Buye. Islamic Art Studies, 10(20), 41–60.
Mohammadi, R. (2010). Studying inscriptions of entry-front lodging in Tehran [Thesis]. Shahid University.
Mohammadi, R., & Ali Rajabi, M. (2011). The survey of entrance inscriptions of Tehran houses from Qajar period to the present. Negareh Journal, 5(15), 19–28.
Mohammadi, H. (2017). Conservation and geometry, very old marriage for Iranian historical building. Archaeology & Anthropology: Open Access, 1(2), 42–48. https://doi.org/10.31031/AAOA.2017.01.000508
Mozaffaripour, N. (2014). Identifying the influencing factors in the view of the entrance of commercial and religious uses on improving the feeling of invitingness (Case study of Tajrish area of Tehran). Journal of Urban-Landscape Research, 1(1), 17–24.
Najafgholipour, N., Etesam, I., & Habib, F. (2017). Check in architectural geometry and proportions of the golden Iran (Case study: Tabriz traditional houses). Urban Management, 16(46), 477–491.
Naseri, H., & Amini Farsani, Z. (2022). An investigation into geometric ratios of the sunken courtyards in traditional Iranian houses (a field study on Yazd and Kashan). Journal of Architecture and Urbanism, 46(1), 58–67. https://doi.org/10.3846/jau.2022.15719
Olivieri, L. M., & Iori, E. (2021). Monumental entrance to Gandharan Buddhist architecture: Stairs and gates from swat. Annali di Ca’ Foscari. Serie Orientale, 57, 197–240. https://doi.org/10.30687/annor/2385-3042/2021/01/009
Page, T., Thorsteinsson, G., & Ha, J. G. (2010). Natural sections in product design. International Journal of Contents, 6(3), 71–82. https://doi.org/10.5392/IJoC.2010.6.3.071
PanjehBashi, E., & Doulab, F. (2018). Study of the features and structure of the embellishments of facades in tiled buildings in Shiraz. Negareh Journal, 13(48), 104–125.
Polpuech, S. (1989). The study of entry in architecture [Thesis]. The Faculty of the Graduate School of the New Jersey Institute of Technology.
Posamentier, A. S., & Ingmar, L. (2007). The fabulous Fibonacci numbers. Prometheus Books.
Sarfaraz, A., Javadi, S., & Alian, A. (2012). The influence of Sassanid art on shapes and inscriptions on façade of Jurjir Mosque. The Monthly Scientific Journal of Bagh-e Nazar, 9(22), 3–10.
Sarwar Islam, N. (2020). The golden ratio. IOSR Journal, 12(2), 36–57.
Shahiri Mehrabad, F. (2013). Entrance in street architecture, the impact of the traditional house entrance on the vitality of the street. In International Conference on Civil Engineering Architecture & Urban Sustainable Development (pp. 1–10). Islamic Azad University, Branch Tabriz.
Shayestefar, M., & Khaleghizadeh, S. (2016). Aesthetic analysis of decorative motifs in Ganjalikhan Caravansary. Tourism Management Studies, 10(29), 95–122.
Sharif, H. R. (2002). Darvazeh Qor’an’: In memory of a city gate. Soffeh, 12(34), 103–117.
Silvayeh, S., Daneshjoo, K., & Farmahin Farahani, S. (2013). Geometry in pre-Islamic Iranian architecture and its manifestation in contemporary Iranian architecture. Naqshejahan, 3(1), 55–66.
Soltanzadeh, H. (1992). The entrance space of the old houses in Tehran (1st ed.). Daftar-i pajūhishhāy-i farhangī.
Tabassi, M., & Fazelnasab, F. (2012). Revisiting the role of thought currents of the Safavid Era in the shaping of the facades of the mosques built based on the principles of Isfahan school of architecture. Journal of Fine Arts: Architecture & Urban Planning, 17(3), 1–10. https://doi.org/10.22059/jfaup.2012.30376
Taravati, G. (2008). Porta: The language of doors [Master’s thesis, University of Waterloo]. UWSpace. http://hdl.handle.net/10012/4113
Vico-Prieto, A. F., Cagigas, A., Rosas, J. M., & Callejas-Aguilera, J. E. (2016). Experimental approach to the study of beauty: The role of golden proportion. Psicologica, 37(2), 187–207.
Wolf, E. M. (2007). Making an entrance: Design philosophy and the entry in western architecture. New York School of Interior Design.
Afradi, K. (2018). Categorizing the design and manufacturing methods of doors and portals in historical structures of rasht from Qajar period until now. Pazhohesh-ha-ye Bastanshenasi Iran, 7(15), 203–218.
Ajami, S., Shahroudi Bahnamiri, A., & Lashgari, R. (2023). Evaluation of the geometric shape of windows in the residential houses with neuroscience approach. Journal of Architectural Thought, 7(13), 155–173.
Akhtaruzzaman, M., & Shafie, A. A. (2011). Geometrical substantiation of Phi, the Golden Ratio and the baroque of nature, architecture, design and engineering. International Journal of Arts, 1(1), 1–22. https://doi.org/10.5923/j.arts.20110101.01
Alsina, C., & Nelsen, R. B. (2010). Charming proofs: A journey into elegant mathematics. Mathematical Association of America. https://doi.org/10.5948/UPO9781614442011
Azar Khordad, F., Hashemi Zarjabad, H., & Zarei, A. (2018). Analysis of applied geometry in the plan of three buildings Abubakr Taybadi, Goharshad Mosque and School of Ghiasieh Khargerd. Parseh Journal of Archaeological Studies, 2(4), 121–136. https://doi.org/10.30699/PJAS.2.4.121
Boettger, T. (2014). Threshold spaces: Transitions in architecture: Analysis and design tools (H. Labies-Volz, Trans.). Walter de Gruyter GmbH. https://doi.org/10.1515/9783038214007
Borges, R. F. (2004). The Phi code in nature, architecture and engineering. WIT Transactions on Ecology and the Environment, 73, 401–409.
Bressler, J. (2020). The ubiquity of Phi in human culture & the natural world. John Carroll University. https://collected.jcu.edu/mastersessays/132
Brown, C. (2008). Fibonacci analysis. Bloomberg Press.
Cui, P., & Huang, M. (2012). Studies on building entrance cold adaption design and structure in cold region – Take Harbin Institute of Architecture as example. Applied Mechanics and Materials, 226–228, 2407–2411. https://doi.org/10.4028/www.scientific.net/AMM.226-228.2407
Danaeinia, A. (2021). The sense of entrance to a place in Kashan historical houses. Journal of Architecture and Urbanism, 45(1), 38–49. https://doi.org/10.3846/jau.2021.13209
Danaeinia, A., & Erfan, B. (2023). The system of theoretical geometry of the two-leged plumb tier of Rasmi-Bandi derived from peripheral circle in Persian architecture. Journal of Conservation and Architecture in Iran, 13(33), 57–76.
Daneshmand, S., & Noghrekar, A. (2012). How to design the entrance of the building according to the principles of the formation of barrier architecture. Journal of Studies on Iranian - Islamic City, (9), 79–89.
Dewitte, L. (2015). Proportionality in the architecture of Dom Bellot. Nexus Network Journal, 17, 457–485. https://doi.org/10.1007/s00004-015-0246-8
Dousti Motlagh, P. (2009). The study of entrance history. Armanshahr Architecture & Urban Development, 2(2), 91–104.
Dunlap, R. A. (1997). The Golden Ratio and Fibonacci numbers. World Scientific Publishing. https://doi.org/10.1142/3595
El-Said, I., & Parman, A. (2008). Geometric concepts in Islamic art (3rd ed., M. Rajabnia, Trans.) Soroush Press.
Farshchi, H., & Majidi, M. (2021). Investigation of the architectural system and geometric proportions of the central courtyard and its walls in the historical houses of Kashan (Case study: Ten historical houses of the Qajar period in Kashan). Culture of Islamic Architecture and Urbanism Journal of Environmental Studies, 6(2), 95–112. https://doi.org/10.52547/ciauj.6.2.95
Feizollahbeig, A., Golabchi, M., & Reza-Zadeh, M. (2021). An investigation in geometry and proportion in relation to structural system in buildings with discontinuous double shell domes in Tafresh region. Soffeh, 31(3), 21–42. https://doi.org/10.52547/sofeh.31.3.21
Fun, T. L., Usman, I. M. S., Utaberta, N., Ariffin, A. R. M., & Sharif, R. (2021). The importance and potential of Golden Ratio in architecture design. Journal of Xi’an University of Architecture & Technology, 13(1), 477–502.
Ganjavie, A. (2003). City entrance of Kerman [Thesis]. Islamic Azad University.
Ghorbani, H. (2021). Golden Ratio: The mathematics of beauty. Mathematics Interdisciplinary Research, 6(2), 159–170.
Gjonbalaj, A., Oliv, D., Lotter, G., & Dalzell, M. (2021). The golden ratio and its effects on the perceived visual appeal of photos. Journal of Student Research, 10(1), 1–13. https://doi.org/10.47611/jsrhs.v10i1.1346
Grütter, J. K. (2009). Ästhetik der architektur (5st ed., Pakzad and A. Homayun, Trans.). Publications Center of Shahid Beheshti University.
Havil, J. (2012). The irrationals: A story of the numbers you can’t count on. Princeton University Press. https://doi.org/10.1515/9780691247670
Javadi Nodeh, M., Shahcheraghi, A., & Andalib, A. (2022). An investigation of the golden proportions and geometric principles derived from nature in the structural components of the traditional houses (Case study: Qajar houses in Ardabil). Bagh-e Nazar, 19(100), 35–48.
Kalantari, N. N., Etesam, I., & Habib, F. (2017). Check in architectural geometry and proportions of the golden Iran (Case study: Tabriz traditional houses). Urban Management, 16(46), 477–491.
Katyal, P., Gupta, P., Gulati, N., & Jain, H. (2019). A compendium of Fibonacci ratio. Journal of Clinical and Diagnostic Research, 13(11), 3–10. https://doi.org/10.7860/JCDR/2019/42772.13317
Karimi Khorasani, K. (2017). Analyze of geometric proportions and structure of girih tiles in portals of schools and shrines of Isfahan (Case study: Nimavar school and Darb-e Imam shrine) [Thesis]. Art University of Isfahan.
Khamechian, A., Azad, M., & Tahbaz, M. (2018). Geometric analysis and proportions of Orosi Windows’s Case study: 7 Orosi of Kashan houses. Journal of Iranian Handicrafts Studies, 2(1), 5–23. https://doi.org/10.22052/1.2.5
Koshy, T. (2018). Fibonacci and Lucas numbers with applications (2nd ed., Vol. 1). John Wiley & Sons, Inc. https://doi.org/10.1002/9781118742297
Krier, R. (2001). Architectural proportions (1st ed., M. Ahmadinejad, Trans.). Nashre Khak.
Larsen, S. H. (2021). DNA structure and the golden ratio revisited. Symmetry, 13(10), Article 1949. https://doi.org/10.3390/sym13101949
Lawlor, R. (1982). Sacred geometry: Philosophy and practice (1st ed.). Thames & Hudson Ltd.
Moblian, E., & Kianmehr, G. (2014). The influence and adaptation of the role of Sasanian motifs on the motifs of the front of the mosque of Jurgir al-Buye. Islamic Art Studies, 10(20), 41–60.
Mohammadi, R. (2010). Studying inscriptions of entry-front lodging in Tehran [Thesis]. Shahid University.
Mohammadi, R., & Ali Rajabi, M. (2011). The survey of entrance inscriptions of Tehran houses from Qajar period to the present. Negareh Journal, 5(15), 19–28.
Mohammadi, H. (2017). Conservation and geometry, very old marriage for Iranian historical building. Archaeology & Anthropology: Open Access, 1(2), 42–48. https://doi.org/10.31031/AAOA.2017.01.000508
Mozaffaripour, N. (2014). Identifying the influencing factors in the view of the entrance of commercial and religious uses on improving the feeling of invitingness (Case study of Tajrish area of Tehran). Journal of Urban-Landscape Research, 1(1), 17–24.
Najafgholipour, N., Etesam, I., & Habib, F. (2017). Check in architectural geometry and proportions of the golden Iran (Case study: Tabriz traditional houses). Urban Management, 16(46), 477–491.
Naseri, H., & Amini Farsani, Z. (2022). An investigation into geometric ratios of the sunken courtyards in traditional Iranian houses (a field study on Yazd and Kashan). Journal of Architecture and Urbanism, 46(1), 58–67. https://doi.org/10.3846/jau.2022.15719
Olivieri, L. M., & Iori, E. (2021). Monumental entrance to Gandharan Buddhist architecture: Stairs and gates from swat. Annali di Ca’ Foscari. Serie Orientale, 57, 197–240. https://doi.org/10.30687/annor/2385-3042/2021/01/009
Page, T., Thorsteinsson, G., & Ha, J. G. (2010). Natural sections in product design. International Journal of Contents, 6(3), 71–82. https://doi.org/10.5392/IJoC.2010.6.3.071
PanjehBashi, E., & Doulab, F. (2018). Study of the features and structure of the embellishments of facades in tiled buildings in Shiraz. Negareh Journal, 13(48), 104–125.
Polpuech, S. (1989). The study of entry in architecture [Thesis]. The Faculty of the Graduate School of the New Jersey Institute of Technology.
Posamentier, A. S., & Ingmar, L. (2007). The fabulous Fibonacci numbers. Prometheus Books.
Sarfaraz, A., Javadi, S., & Alian, A. (2012). The influence of Sassanid art on shapes and inscriptions on façade of Jurjir Mosque. The Monthly Scientific Journal of Bagh-e Nazar, 9(22), 3–10.
Sarwar Islam, N. (2020). The golden ratio. IOSR Journal, 12(2), 36–57.
Shahiri Mehrabad, F. (2013). Entrance in street architecture, the impact of the traditional house entrance on the vitality of the street. In International Conference on Civil Engineering Architecture & Urban Sustainable Development (pp. 1–10). Islamic Azad University, Branch Tabriz.
Shayestefar, M., & Khaleghizadeh, S. (2016). Aesthetic analysis of decorative motifs in Ganjalikhan Caravansary. Tourism Management Studies, 10(29), 95–122.
Sharif, H. R. (2002). Darvazeh Qor’an’: In memory of a city gate. Soffeh, 12(34), 103–117.
Silvayeh, S., Daneshjoo, K., & Farmahin Farahani, S. (2013). Geometry in pre-Islamic Iranian architecture and its manifestation in contemporary Iranian architecture. Naqshejahan, 3(1), 55–66.
Soltanzadeh, H. (1992). The entrance space of the old houses in Tehran (1st ed.). Daftar-i pajūhishhāy-i farhangī.
Tabassi, M., & Fazelnasab, F. (2012). Revisiting the role of thought currents of the Safavid Era in the shaping of the facades of the mosques built based on the principles of Isfahan school of architecture. Journal of Fine Arts: Architecture & Urban Planning, 17(3), 1–10. https://doi.org/10.22059/jfaup.2012.30376
Taravati, G. (2008). Porta: The language of doors [Master’s thesis, University of Waterloo]. UWSpace. http://hdl.handle.net/10012/4113
Vico-Prieto, A. F., Cagigas, A., Rosas, J. M., & Callejas-Aguilera, J. E. (2016). Experimental approach to the study of beauty: The role of golden proportion. Psicologica, 37(2), 187–207.
Wolf, E. M. (2007). Making an entrance: Design philosophy and the entry in western architecture. New York School of Interior Design.